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Echo Chamber Incites Online Mob to Attack Math Profs

There’s evidence for greater variability in the distribution of men, compared to women, in various domains. Two math professors, Theodore Hill and Sergei Tabachnikov, wrote an article exploring a mathematical model for the evolution of this difference in variation, and send the article to the Mathematical Intelligencer, a magazine that welcomes “expository articles on all kinds of mathematics, and articles that portray the diversity of mathematical communities and mathematical thought, emergent mathematical communities around the world, new interdisciplinary trends, and relations between mathematics and other areas of culture.” After some revision, the article was accepted for publication. But then there was pushback from activists within the academic community, and a few months later the editor of the magazine informed the authors that article would not be published; also one of the authors, Tabachnikov, removed himself from the paper out of fear of reprisals from his university. (There also seems to possibly have been a third author who also backed out of the paper, but there’s less detail on that part.) There was an online furor, and a month later, the remaining author, Hill was contacted by the editor of the online New York Journal of Mathematics and invited to submit the article there. (The NYJM, unlike the Intelligencer, seems to focus entirely or nearly entirely on pure math, at least that’s what I see here.) A month later, after a referee report and some revisions, the paper appeared online at NYJM. But then, three days later, the article was removed from that journal’s website and replaced by a completely different article on an unrelated topic. Currently the paper is available on Arxiv.

All the above happened in 2017. During the following months, Hill tried to find out what happened. He ended up with the impression that there had been a politically-motivated campaign against his paper, causing it to be yanked from the Intelligencer and the NYJM as the result of an intimidation campaign by academic activists. Then last week he wrote up the whole story as a blog entry or online article at the site Quillette. I first heard about the story when a couple people pointed me to Hill’s post.

The math paper in question

I was curious so I followed the link to the Arxiv paper, “An Evolutionary Theory for the Variability Hypothesis,” by Theodore Hill, dated 24 Aug 2018.

Hill’s article did not strike me as mathematically deep, not did it seem politically objectionable in any way. The math was accessible and related to an interesting general issue, so I could see how it would be of interest to a general-interest mathematics magazine such as the Intelligencer. In some ways it reminded me of my paper, “Forming voting blocs and coalitions as a prisoner’s dilemma: a possible theoretical explanation for political instability,” which I published in an econ journal back in 2003: My article, like Hill’s, contained some mathematical results that were inspired by a real phenomenon of interest, and although the connection between the math and anything in the real world was tenuous, I (and, correspondingly, Hill) thought the mathematical results were interesting enough, and the motivating applied problem compelling enough, that our efforts were worth sharing with the world. I later followed up that paper with work of more applied relevance, and I’m supportive of the general idea of working out mathematical models, as long as we recognize their limitations, as Hill does in his paper (“the contribution here is also merely a general theory intended to open the discussion to further mathematical modeling and analysis”). So I could see why the Intelligencer might want to publish the paper. I could also see why they might not want to publish it, as the mathematical argument in the paper is pretty simple, and the paper is also loaded down with what seem to me to be irrelevant claims regarding biology and society. I didn’t find these claims political or offensive; they just seemed beside the point in a math paper. I think it would be enough to just raise the issue (more variability among men than women in various traits), give some references, and move on from there, rather than attempt a review of the biology literature on the topic. Anyway, the paper seemed innocuous to me: not so exciting, but with some mathematical content; on an interesting topic even if with some difficulties linking the math to the biology; reasonable enough to publish in the Intelligencer.

Trying to make sense of the story

With this in mind, there were a few aspects of Hill’s blog entry that didn’t completely make sense to me.

First, the research article did not seem politically objectionable to me. I could see how people with strong views on the topic of sex differences would find things to criticize in his paper, and he could well be missing some important points of the biology, and if you really tried to apply his model to data I don’t think it would work at all, so, sure, the paper’s not perfect. But as a math paper that touches on an interesting topic, it is what it is, and I was surprised there’d be a campaign to suppress it.

Second, some of the details didn’t quite line up. For example, Hill wrote that the Marjorie Senechal, the editor of the Intelligencer, “suggested that we might enliven our paper by mentioning Harvard President Larry Summers . . . With her editorial guidance, our paper underwent several further revisions until, on April 3, 2017, our manuscript was officially accepted for publication.” But none the versions of the paper I saw on Arxiv mentioned Summers. (Here’s the version time-stamped 19 Mar 2017, which is the closest to that April 3 acceptance date.) So I feel like we’re not actually getting to see the version of the paper that got all the controversy. The other detail that I couldn’t quite follow was why the paper would’ve appeared in NYJM, which seems to only publish stuff like “A dyadic Gehring inequality in spaces of homogeneous type and applications” and “Off-diagonal sharp two-weight estimates for sparse operators.”

The thing I couldn’t quite figure out was why this paper bothered people so much. But, upon reflection, I think I have an idea. I’m a political scientist, and one thing that annoys the hell out of me is when people apply cute but wrong math arguments to real political questions. For example, there was that claim that the probability of casting a decisive vote is on the order of 10 to the −2,650th power, or misinformed but authoritative-sounding claims about the voting patterns of rich and poor. So I could see how someone who’s really studied sex differences could find Hill’s model to be annoying enough that they’d not want it spread around the world with the imprimateur of a serious journal. Sex differences isn’t my area of research so I was just considering Hill’s paper as expressing a simple and somewhat interesting mathematical model. If I saw the same kind of model applied to voting (for example, using the binomial probability model to compute the probability of a decisive vote), I’d be screaming. I wouldn’t want a journal to publish such a model, and if it were published, I’d want to run some article alongside explaining why the model doesn’t make sense. Not that the math is wrong but that it doesn’t apply here. I’m not prepared to make that judgment one way or another for the Hill and Tabachnikov paper, but my guess is that that’s where the critics are coming from. It’s not about suppressing a politically offensive idea; it would be more, from their perspective, about not spreading a mistaken idea. And it probably didn’t help that early versions of the paper said, “there has been no clear or compelling explanation offered for why there might be gender differences in variability,” which seems like a pretty strong claim regarding the biology literature. See this post from mathematician Timothy Gowers.

The big thing, though, was the paper getting accepted and then yanked—twice. Once from the Intelligencer and once from the NYJM. It’s hard to imagine a good reason for that.

The other thing that I noticed in Hill’s blog post was Lee Wilkinson, an influential statistician (among other things, author of The Grammar of Graphics, which motivated R’s ggplot package) and friend of mine, who was identified as the father of mathematician Amie Wilkinson, who in turn, according to Hill, “had successfully suppressed my variability hypothesis research and trampled on the principles of academic liberty.” Hill also wrote that Amie Wilkinson’s husband, Benson Farb, another math professor, “had written a furious email” to the NYJM editor demanding that Hill’s paper “be deleted at once.”

It was hard for me to put all the pieces together. I could see how the Intelligencer would want to publish the paper and I could see how others would think the paper not appropriate to publish (for scientific, not political, reasons). Both those views made sense to me, as they represented slightly different perspectives on the value of a work of applied mathematics. But I couldn’t see why there’d be a movement of the radical academic Left to suppress the paper—for one thing, there already have been lots and lots of papers published in reputable journals on sex differences in general and the greater-male-variability hypothesis in particular, so why would the Left focus such effort on a little math paper; and, for another, the article did not seem politically offensive.

The tempest

Hill’s post appeared on 7 Sep. In the following days, the story was featured in a blog post at Reason magazine by law professor David Bernstein (“A Mathematics Paper Two Math Journals Were Mau-Maued into Suppressing”), tweets by psychology professors Jordan Peterson (“Here’s the offending paper. Please read and distribute as widely as possible”) and Steven Pinker (“Again the academic left loses its mind: Ties equality to sameness, erodes credibility of academia, & vindicates right-wing paranoia”), and various other places on the web, including lots of material too horrible to quote (you can google and look for it yourself if you’re interested).

Many of these comment and twitter threads, including the one attached Hill’s post on the Quillette site, featured personal attacks on Amie Wilkinson and Benson Farb. Some of the personal attacks are just horrible. I won’t quote them here—you can find these remarks yourself if you want—because they’re not directly relevant to what happened to Hill. After all, if Wilkinson and Farb really did behave badly and try to suppress an already-published paper (which is much different that the very routine action of recommended that a submitted paper not be accepted for publication, or recommending that a published or in-press paper be accompanied by a rebuttal), then such suppressive actions would not be justified after the fact by others’ bad behavior toward them. The attacks on Wilkinson and Farb bothered me because of their virulence, and they give me some sense of the kind of people who comment at the site where Hill posted, that’s all. In the context of some quarters of the internet, the criticisms that Hill made are like waving the proverbial red flag in front of the bull.

On 11 Sep—4 days after Hill posted his story—Amie Wilkinson and Benson Farb posted their sides of the story. Wilkinson wrote: “I first saw the publicly-available paper of Hill and Tabachnikov on 9/6/17, listed to appear in The Mathematical Intelligencer. . . . I sent an email, on 9/7/17, to the Editor-in-Chief . . . In it, I criticized the scientific merits of the paper and the decision to accept it for publication, but I never made the suggestion that the decision to publish it be reversed. Instead, I suggested that the journal publish a response rebuttal article by experts in the field to accompany the article. One day later, on 9/8/17, the editor wrote to me that she had decided not to publish the paper. . . . I had no involvement in any editorial decisions concerning Hill’s revised version of this paper in The New York Journal of Mathematics.”

Farb wrote: “This statement is meant to set the record straight on the unfounded accusations of Ted Hill regarding his submission to the New York Journal of Mathematics (NYJM), where I was one of 24 editors serving under an editor-in-chief. Hill’s paper raised several red flags to me and other editors, giving concern not just about the quality of the paper, but also the question of whether it underwent the usual rigorous review process. . . . At the request of several editors, the editor-in-chief pulled the paper temporarily on 11/9/17 so that the entire editorial board could discuss these concerns. . . . The editor who handled the paper was asked to share these reports with the entire board. . . . The reports themselves were not from experts on the topic of the paper. They did not address our concerns about the substantive merit of the paper. . . . Further, the evidence that the paper had undergone rigorous scrutiny before being accepted was scant. In light of this, the board voted (by a 2-to-1 ratio) to rescind the paper.”

Working out what really happened

OK, now we can put all the pieces together. This is not a “he-said, she-said” or “Rashomon” situation in which different people present us with incompatible stories, and we have no way to reconcile their stories. One thing that’s interesting about these stories is how consistent they are with each other.

Look back at Hill’s post and distinguish what he knows directly—what happened to him—and where he is speculating. What happened for sure is that his paper was accepted, then yanked, from two separate journals. The rest is second-hand. The academic Left, the attacks on the NYJM, the “the husband-wife team who had successfully suppressed my variability hypothesis research and trampled on the principles of academic liberty,” the claim that his paper was judged based on “desirability or political utility”—Hill has no direct evidence for that.

Indeed, the facts of Hill’s story are consistent with the facts of Wilkinson’s and Farb’s story. Here’s what happened. Or, at least, the following is consistent with what was recounted by Hill, Wilkinson, and Farb:
– Hill’s paper was accepted by the Intelligencer and posted online. Wilkinson felt the paper was flawed and suggested the paper be published with a rebuttal. Instead, the journal editor un-published the paper.
– Hill’s paper was accepted by the NYJM in an unusual fashion by one of the journal’s 24 editors. After a review of the editorial process, the full editorial board un-published the paper.

Hill is annoyed, and justifiably so. For a journal editor to accept his paper, then reject it, that’s not cool. It’s happened to me a couple of times, and it pisses me off, to put in all the work of writing an article, going through the review process, finally the paper appears or is scheduled to appear, and then, Bam! the journal pulls the rug out from under you.

The problem is that Hill is focusing his annoyance on the wrong people. And there’s a clue in Hill’s own post, where he writes, “My quarrel, the vice-provost [of the University of Chicago] concluded, was with the editors-in-chief who had spiked my papers . . .” That’s right! The problem is with the editors who broke the rules, it’s not with reviewers who raised concerns.

Can the rabble-rousers call off the online mob?

To me, the most unfortunate part of the story is the amplification of Hill’s post throughout Twitter, Quillette, 4chan, etc., abetted by thought leaders on Twitter, leading to noxious hatred spewed at Amie Wilkinson. I don’t blame Jordan Peterson, Steven Pinker, or the editors of Quillette for the behavior of Twitter commenters, or even for the behavior of commenters at Quillette. But now that more of the story is out, it’s time for all these people to explain what happened to their followers, and to apologize.

Theodore Hill and Amie Wilkinson clearly differ on the value of the Hill and Tabachnikov paper, both as mathematics and regarding its relevance to biology and the study of human institutions. For example, Wilkinson wrote, “Invoking purely mathematical arguments to explain scientific phenomena without serious engagement with science and data is an offense against both mathematics and science.”

But they agree on the value of open communication.

Here’s Wilkinson: “I believe that discussion of scientific merits of research should never be stifled. This is consistent with my original suggestion to bring in outside experts to rebut the Hill-Tabachnikov paper.” The fact that a journal editor pulled Hill’s paper, after Wilkinson recommended otherwise, reflects poorly on the editor, not on the other people involved in this story. But that’s not the story Hill, or the online mob, wanted to hear.